A data assimilation framework to predict the response of glioma cells to radiation

We incorporate a practical data assimilation methodology into our previously established experimental-computational framework to predict the heterogeneous response of glioma cells receiving fractionated radiation treatment. Replicates of 9L and C6 glioma cells grown in 96-well plates were irradiated with six different fractionation schemes and imaged via time-resolved microscopy to yield 360- and 286-time courses for the 9L and C6 lines, respectively. These data were used to calibrate a biology-based mathematical model and then make predictions within two different scenarios. For Scenario 1, 70% of the time courses are fit to the model and the resulting parameter values are averaged. These average values, along with the initial cell number, initialize the model to predict the temporal evolution for each test time course (10% of the data). In Scenario 2, the predictions for the test cases are made with model parameters initially assigned from the training data, but then updated with new measurements every 24 hours via four versions of a data assimilation framework. We then compare the predictions made from Scenario 1 and the best version of Scenario 2 to the experimentally measured microscopy measurements using the concordance correlation coefficient (CCC). Across all fractionation schemes, Scenario 1 achieved a CCC value (mean ± standard deviation) of 0.845 ± 0.185 and 0.726 ± 0.195 for the 9L and C6 cell lines, respectively. For the best data assimilation version from Scenario 2 (validated with the last 20% of the data), the CCC values significantly increased to 0.954 ± 0.056 (p = 0.002) and 0.901 ± 0.061 (p = 8.9e-5) for the 9L and C6 cell lines, respectively. Thus, we have developed a data assimilation approach that incorporates an experimental-computational system to accurately predict the in vitro response of glioma cells to fractionated radiation therapy.


Supplementary
Figure S1.Radiation treatment schedule.Cells are seeded and incubated overnight before treatment.On Day 0, the cells are irradiated with either a total of 16 Gy or 20 Gy via different schedules.In the 16 Gy group, the cells receive either two fractions of 8 Gy, three fractions of 5.3 Gy, or four fractions of 4 Gy.In the 20 Gy group, the cells receive either two fractions of 10 Gy, three fractions of 2 Gy, or four fractions of 5 Gy.All fractions are separated by 24 hours.We refresh the cell culture media on Days 5 and 10.Microscopy images are collected continuously right after the first fraction on Day 0 until the end of Day 13.Conversion rate from proliferation to senescent components Note: A units value of "1" indicates the parameter is dimensionless.global prediction is performed by using only X pop , which is equal to setting the weights on X ind,i to 0 throughout the time course.In panel (b), we increase the weights linearly as in Eq. ( 11).In panel (c), we increase the weights quadratically via Eq.( 13).Compared to the linear weighting, the quadratic weighting scheme emphasizes the sample-specific measurements earlier in the time course.

S5. 9L validation group versus testing group accuracy.
To understand why the accuracy of 9L validation group (0.953 ± 0.052) is better compared to its testing group (0.950 ± 0.049), which is not common in learning models, we checked the accuracy of 9L validation group and testing group for each treatment conditions, and acquired the following numbers (mean ± standard deviation): a) four fractions of 4 Gytesting (0.961 ± 0.027), validation (0.960 ± 0.029) b) three fractions of 5.3 Gytesting (0.878 ± 0.050), validation (0.875 ± 0.092) c) two fractions of 8 Gytesting (0.916 ± 0.041), validation (0.942 ± 0.036) d) four fractions of 5 Gytesting (0.984 ± 0.004), validation (0.984 ± 0.002) e) three fractions of 6.7 Gytesting (0.986 ± 0.005), validation (0.986 ± 0.005) f) two fractions of 10 Gy --testing (0.977 ± 0.013), validation (0.974 ± 0.010).This confirms that the slight difference only comes from the two fractions of 8 Gy group of the 9L cell lines.We then checked the original data and there were no curious differences found.However, we do notice the following: because the testing group only includes 36 9L samples in total as mentioned in the Methods section (and only 6 samples are from two fractions of 8 Gy group), a 'bad prediction' curve may greatly affect this value.In fact, there are two such curves in these six samples (with CCCs of only 0.857 and 0.891, respectively).By removing these two 'bad examples', the average of the remaining four curves achieves 0.947 ± 0.027.We thus believe this slight difference is due to the two outliers and small sample size used in our testing set.

Figure S2 .
Figure S2.Illustrating different methods of weighting the individual parameters.In panel (a),global prediction is performed by using only X pop , which is equal to setting the weights on X ind,i to 0 throughout the time course.In panel (b), we increase the weights linearly as in Eq. (11).In panel (c), we increase the weights quadratically via Eq.(13).Compared to the linear weighting, the quadratic weighting scheme emphasizes the sample-specific measurements earlier in the time course.

Figure S3 .
Figure S3.The data assimilation prediction versus global prediction for all 9L samples from the validation group.See caption to Figure 6 for an explanation of the results.

Figure S4 .
Figure S4.The data assimilation prediction versus global prediction for all C6 samples from the validation group.See caption to Figure 6 for an explanation of the results.